On computing periodic coprime factorizations

Numerically reliable state space algorithms are proposed for computing coprime factorizations of periodic descriptor systems. Two factorizations are considered for causal periodic descriptor systems: stable coprime factorizations and coprime factorizations with inner denominators. The corresponding algorithms are based on a recursive generalized periodic Schur method for eigenvalue assignment. For general descriptor periodic systems an algorithm is proposed to compute factorizations with causal (proper) factors. This algorithm relies on computing suitable right annihilators of appropriate extended systems. The proposed algorithms are lifting-free and generally applicable regardless the original periodic descriptor state space representations are minimal or not.